mlsanityData to 14 Oct 2026

Deep Signature Algorithm for Multi-dimensional Path-Dependent Options

arXiv 2211.11691 ↗First posted 21 Nov 2022q-fin.CP cs.LG q-fin.MFcited by 6

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Abstract (arXiv)

In this work, we study the deep signature algorithms for path-dependent options. We extend the backward scheme in [Hur'e-Pham-Warin. Mathematics of Computation 89, no. 324 (2020)] for state-dependent FBSDEs with reflections to path-dependent FBSDEs with reflections, by adding the signature layer to the backward scheme. Our algorithm applies to both European and American type option pricing problems while the payoff function depends on the whole paths of the underlying forward stock process. We prove the convergence analysis of our numerical algorithm with explicit dependence on the truncation order of the signature and the neural network approximation errors. Numerical examples for the algorithm are provided including: Amerasian option under the Black-Scholes model, American option with a path-dependent geometric mean payoff function, and the Shiryaev's optimal stopping problem.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 11 of its 50 references that are in the map. First posted on arXiv 21 Nov 2022.

Builds on

11 of 50 references.

References · 11

  1. 2017Solving high-dimensional partial differential equations using deep learningcited by 556
  2. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
  3. 2019Deep Signature Transformscited by 75
  4. 2018Convergence of the Deep BSDE Method for Coupled FBSDEscited by 43
  5. 2021Optimal Stopping via Randomized Neural Networkscited by 28
  6. 2019Solving high-dimensional optimal stopping problems using deep learningcited by 22
  7. 2022Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problemscited by 9
  8. 2022Deep neural network expressivity for optimal stopping problemscited by 9
  9. 2022Deep BSDE-ML Learning and Its Application to Model-Free Optimal Controlcited by 6
  10. 2021Deep Signature FBSDE Algorithmcited by 4
  11. 2022A neural network approach to high-dimensional optimal switching problems with jumps in energy marketscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 0; 2025: 2; 2026: 3.

6 papers.

  1. 2023Recent Developments in Machine Learning Methods for Stochastic Control and Gamescited by 24
  2. 2025Deep Neural Operator Learning for Probabilistic Modelscited by 3
  3. 2025Global universal approximation with Brownian signaturescited by 2
  4. 2026Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signalscited by 0
  5. 2026Forward Trajectory Steering for Hamilton-Jacobi Reachability Analysiscited by 0
  6. 2026Deep Learning for Reflected BSDEs: Regularization and Error Analysiscited by 0